Journal of Mathematical Chemistry

, Volume 57, Issue 1, pp 149–179 | Cite as

Numerical simulation for computational modelling of reaction–diffusion Brusselator model arising in chemical processes

  • Sanjay Kumar
  • Ram JiwariEmail author
  • R. C. Mittal
Original Paper


The main focus of this article is to capture the patterns of reaction–diffusion Brusselator model arising in chemical processes such as enzymatic reaction, formation of turing patterns on animal skin, formation of ozone by atomic oxygen through a triple collision. For this purpose, a meshfree algorithm is developed based on radial basis multiquadric functions and differential quadrature (DQ) technique. The algorithm is more general than (Alqahtani in J Math Chem 56:15431566, 2018) due to meshfree and \(C^{\infty }\) properties of radial basis functions. Numerical experiment section support the accuracy and efficiency of the algorithm. The computed results satisfy the theory of Brusselator model which says for small values of diffusion coefficient, the steady state solution converges to equilibrium point \(\left( \alpha , \dfrac{\beta }{\alpha }\right) \) if \(1-\beta +\alpha ^{2}>0\) .


Brusselator model Oscillating reactions Mesh free algorithm Stability analysis Numerical experiments 



The work is supported by Science and Engineering Research Board (SERB) with Grant No. SERB/YSS/2015/000599.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology RoorkeeRoorkeeIndia

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